Simplify the following expression: $ a = \dfrac{5z - 1}{4z} + \dfrac{-7}{5} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{5z - 1}{4z} \times \dfrac{5}{5} = \dfrac{25z - 5}{20z} $ Multiply the second expression by $\dfrac{4z}{4z}$ $ \dfrac{-7}{5} \times \dfrac{4z}{4z} = \dfrac{-28z}{20z} $ Therefore $ a = \dfrac{25z - 5}{20z} + \dfrac{-28z}{20z} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{25z - 5 - 28z}{20z} $ $a = \dfrac{-3z - 5}{20z}$